On Wed, 28 Apr 2010, Zooko O'Whielacronx wrote:
Anyway, although this is not one, there do exist proposals for public key crypto schemes where breaking the scheme implies solving a worst case instance of a supposedly hard problem, right?
Not to worst-case hardness of an NP-complete problem, no. Quite the contrary, there has been some body of work showing that a result of this sort is unlikely. (Though, as with all things related to complexity theory where our state of knowledge is so limited, such a statement must be taken wit ha grain of salt. In any case, such a result is well beyond anything we can currently prove.)
2. some kind of strong argument that it really is secure (the gold standard would be reduction to a worst-case instance of an NP-complete problem)
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